Flying to New England for a while, so continuing with extra short posts. For today, here is a (I think) nice question I gave for my linear algebra class last summer, as a problem meant to encourage the use of technology:
It is clear that any 2 x 2 matrix, each of whose entries is a distinct prime, will be nonsingular. For example, the matrix
is nonsingular. However, there exist 3 x 3 matrices, each of whose entries is a distinct prime, which are singular. For example, the matrix
Out of all such matrices (3 x 3, distinct prime entries, singular), which one has the smallest sum of entries? (where the solution will be this sum, since exchanging rows/columns will leave the determinant and sum invariant, but shows that the actual matrix will be nonunique)
Solution Friday. As an aside, I have only upper bounds for the 4 x 4 case.